### Skapa referens, olika format (klipp och klistra)

**Harvard**

Deijfen, M. och Meester, R. (2006) *Generating stationary random graphs on Z with prescribed independent, indentically distributed degrees*.

** BibTeX **

@article{

Deijfen2006,

author={Deijfen, Maria and Meester, R.},

title={Generating stationary random graphs on Z with prescribed independent, indentically distributed degrees},

journal={Advances in Applied Probability},

issn={00018678 },

volume={38},

issue={2},

pages={287-298},

abstract={Let F be a probability distribution with support on the nonnegative integers. We describe two algorithms for generating a stationary random graph, with vertex set ℤ, in which the degrees of the vertices are independent, identically distributed random variables with distribution F. Focus is on an algorithm generating a graph in which, initially, a random number of 'stubs' with distribution F is attached to each vertex. Each stub is then randomly assigned a direction (left or right) and the edge configuration obtained by pairing stubs pointing to each other, first exhausting all possible connections between nearest neighbors, then linking second-nearest neighbors, and so on. Under the assumption that F has finite mean, it is shown that this algorithm leads to a well-defined configuration, but that the expected length of the shortest edge attached to a given vertex is infinite. It is also shown that any stationary algorithm for pairing stubs with random, independent directions causes the total length of the edges attached to a given vertex to have infinite mean. Connections to the problem of constructing finitary isomorphisms between Bernoulli shifts are discussed.},

year={2006},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 102542

A1 Deijfen, Maria

A1 Meester, R.

T1 Generating stationary random graphs on Z with prescribed independent, indentically distributed degrees

YR 2006

JF Advances in Applied Probability

SN 00018678

VO 38

IS 2

SP 287

OP 298

AB Let F be a probability distribution with support on the nonnegative integers. We describe two algorithms for generating a stationary random graph, with vertex set ℤ, in which the degrees of the vertices are independent, identically distributed random variables with distribution F. Focus is on an algorithm generating a graph in which, initially, a random number of 'stubs' with distribution F is attached to each vertex. Each stub is then randomly assigned a direction (left or right) and the edge configuration obtained by pairing stubs pointing to each other, first exhausting all possible connections between nearest neighbors, then linking second-nearest neighbors, and so on. Under the assumption that F has finite mean, it is shown that this algorithm leads to a well-defined configuration, but that the expected length of the shortest edge attached to a given vertex is infinite. It is also shown that any stationary algorithm for pairing stubs with random, independent directions causes the total length of the edges attached to a given vertex to have infinite mean. Connections to the problem of constructing finitary isomorphisms between Bernoulli shifts are discussed.

LA eng

DO 10.1239/aap/1151337072

LK http://dx.doi.org/10.1239/aap/1151337072

OL 30